Vater and Maltebrun have given a few hundred examples of such analogies: and the systematic writers have supposed that they had exhausted the comparisons. Yet a single language, the Chilian, has by itself more affinities with the languages of Europe, than all those mentioned by Vater and others, put together! The foreign or transatlantic affinities of American languages, vary from 10 to 70 per cent, according to the nations. If we suppose that there are 400 languages in America, and as many in the eastern hemisphere, and each to have about 2000 roots or essential words only; while the mean affinities are only 25 per cent: we shall find as many as 200,000 affinities! out of America, in every American language; and in all the 400, as many as 80 millions! instead of the paltry reckoning of 1000 or so. All this is susceptible of mathematical proofs, and shall be unfolded gradually in these pages. The theory about the common exclusive grammatical structure of all the American languages, is equally erroneous and based upon partial facts. Instead of all the American languages being polysynthetic by amalgamating words, we find in America many mixt forms, and even the pure monosylabic: while the amalgamation of words prevails more or less in Europe and Africa; chiefly in the Bask, Italian dialects, Greek, Berber and other Atlantic dialects, the Negro languages, those of Caffraria, the Sanscrit and all the derived languages. It had been asserted that no American language was monosylabic: yet Balbi states that the Guarani and Maya are such; Nasera has lately proved the same of the Othomi. Thus we have at least 3 such American groups of languages. But there are more; nay many American languages have monosylabic roots, even among the most amalgamated groups. The most obvious grammatical classification of American languages, has escaped the acuteness of philologists. I find it in the epithetic structure, or relative position of ideas. Under this view all the languages arrange themselves in three great classes or groups. 1. Regular, 2. Resupinate, 3. Mixt. 1. _The Regular_ is the most simple and natural form: where the roots or nouns are prefixed, and the adjuncts or adjectives, expressing epithetes or qualities follow or are added. This group includes in the Eastern Continent 1. All the Semetic languages, Arabic, Hebrew, &c. 2. All the Atlantic and Egyptian languages. 3. All the Celtic and Cantabrian languages. 4. All the Polynesian and Malay languages. 5. The Bhotiya and many languages of Thibet. 6. Most of the Negro languages. 7. Yakut of Siberia, &c. In America this group includes my groups 1. Innuit or Uski. 2. Ongwi. 3. Capaha. 4. Chactah. 5. All the languages related thereto in North-west America, the Kaluchi, Mandan, &c. 6. All the Guarani languages of South America, and perhaps many others, Mayna, Mobima, &c.